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Frobenius made many important contributions to mathematics in the latter part of the 19th century. Hawkins here focuses on his work in linear algebra and its relationship with the work of Burnside, Cartan, and Molien, and its extension by Schur and Brauer. He also discusses the Berlin school of mathematics and the guiding force of Weierstrass in that school, as well as the fundamental work of d'Alembert, Lagrange, and Laplace, and of Gauss, Eisenstein and Cayley that laid the groundwork for Frobenius's work in linear algebra. The book concludes with a discussion of Frobenius's contribution to the theory of stochastic matrices
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Sources and Studies in the History of Mathematics and Physical Sciences Thomas Hawkins The Mathematics of Frobenius in Context A Journey Through 18th to 20th Century Mathematics The Mathematics of Frobenius in Context Sources and Studies in the History of Mathematics and Physical Sciences For further volumes: http://www.springer.com/series/4142 Thomas Hawkins The Mathematics of Frobenius in Context A Journey Through 18th to 20th Century Mathematics 123 Thomas Hawkins Department of Mathematics & Statistics Boston University Boston, MA, USA ISBN 978-1-4614-6332-0 ISBN 978-1-4614-6333-7 (eBook) DOI 10.1007/978-1-4614-6333-7 Springer New York Heidelberg Dordrecht London Library of Congress Control Number: 2013941038 © Springer Science+Business Media New York 2013 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com) Preface This book grew out of my research on the history of mathematics over the past 40 years. Time and again, the path of my investigation led me to the consideration of work by Frobenius that played an important role in the historical development I was attempting to understand. I finally decided it would be appropriate to bring these research experiences together into a book on the mathematics of Frobenius, especially since little has been written about him despite the fact that he made many important contributions to present-day math